A Modeling of Toms Effect Based on the Discrete Element Model

基于离散元模型，建立了聚合物或表面活性剂稀加减阻（Toms效应）的数值模拟模型。与流体的速度波动相比，代表聚合物或棒状胶束的离散单元的尺寸非常小。因此，假设单元在流体中处于平衡状态，并转向速度梯度张量的特征向量的方向。并将离散单元的宏观效应建模为应力，假设单元之间相互独立。采用刚性哑铃单元作为离散单元模型，对该模型进行了直接数值模拟，结果表明，该模型的减阻率可达37%。此外，以下是结论性意见。（1）减阻可以在不假设形成为细长聚合物网络或棒状胶束的宏观结构的情况下再现。（2）在不考虑弹性的情况下，可以再现流体的减阻和应力亏损现象，并在模型中加入了新的特性，如模拟聚合物的哑铃形单元可以被流体中的拉伸力切割。对Re_τ=120-600的二维槽道流进行了数值模拟，并再现了减阻率达50%的减阻效果。

A model to simulate the drag reductoin by dilute addition of polymer or surfactant (Toms effect) is proposed based on the discrete element model. The dimension of the discrete element, which represents the polymer or the rod-like micelle, is very small compared to that of the velocity fluctuation of the fluid. So it is assumed that the element is in equilibrium state in the fluid and turns to the direction of an eigenvector of the velocity gradient tensor. And the macroscopic effect of the discrete elements is modeled as the stress assuming the elements are independent each other. Direct numerical simulations are carried out with this new model using the rigid dumbbell element as a discrete element model and it is shown that the drag reduction up to 37% drag reduction rate is reproduced. In addition the followings are indicated as concluding remarks. (1)The drag reduction can be reproduced without assuming the macrostructures formed as the network of elongated polymers or rod-like micelles. (2)The drag reduction and the stress deficit can be reproduced without the elasticity.In addition study, new character is added on the model, say, the dumbbell element which simulate a polymer can be cut by the stretching force in the fluid. Simulations of 2D channel flows (Re_τ=120-600) are carried out and the drag reduction up to 50% drag reduction rate is reproduced by the modified model.